When I read Richard Preston’s The Hot Zone in the mid-1990s, I was terrified. This was the first I had heard of a scary new disease called ebola. I was working for an AIDS Service Organization at the time, so I understood — better than most — how blood-borne infectious diseases are contracted. Still, the images of how the victims of this virus die are still with me. Horrifying.

But I’m not at all afraid of ebola today. Not one little bit. Why? Math.

It’s difficult for ebola to spread. Really difficult. Like HIV, the ebola virus only lives in bodily fluids, including blood, saliva, mucus, vomit, semen, breast milk, sweat, tears, feces and urine. (HIV is only transmitted through four bodily fluids: semen, vaginal fluids, breast milk and blood.) Transmission can occur when infected bodily fluids come into contact with a person’s eyes, mouth or nose, or an open wound or abrasion.

Compare this to measles, which is transmitted through the air. The measles virus lives in the mucus lining of the nose. A sneeze or cough can release virus-infected droplets into the air. Breathe in the air with little measles droplets, and unless you’ve been vaccinated, it’s very likely you’ll see a tell-tale rash in a few days.

Since measles is highly contagious for four days before symptoms appear, a person can transmit the virus without even knowing he has it himself. According to the CDC, measles is so contagious that if one person has it, it will spread to 90 percent of the people who come in contact with that person (if they are not already immune, thanks to the vaccine).

It’s All About the R0

The way a virus is transmitted helps determine how contagious the disease is. And the big deal here is something called R0 or “reproduction number” (also called “r-naught”). R0 is the number of people that one infected person will likely infect during an outbreak.

Those of us of a certain age might remember a shampoo commercial that illustrates this perfectly.

Like Fabrerge Organics shampoo, ebola’s R0 is 2. When one person contracts ebola, it is likely that two others will become infected. Yes, those numbers add up — and they have in parts of Africa.

Now take a look at measles, with an R0 of 18. When one person gets measles, it’s likely that 18 people around him do too. Then each of those 18 people spread the virus to 18 more people. In one generation of this infection, 18 x 18 (324) have contracted measles. That’s compared to only 2 x 2 (4) people who will likely contract ebola in one generation of the infection. In fact, measles is still one of the leading causes of death in children around the world. According to the WHO:

Measles is still common in many developing countries – particularly in parts of Africa and Asia. More than 20 million people are affected by measles each year. The overwhelming majority (more than 95%) of measles deaths occur in countries with low per capita incomes and weak health infrastructures.

But measles is not a major threat in the U.S., and we all know why — the measles vaccine. Ebola has no vaccine, but a relatively strong health care system in our country and its very low R0 makes ebola a low threat, compared to other viruses, like HIV and certain strains of influenza.

The scary thing about ebola is not how quickly it spreads but how basic medical care can keep it from spreading. We have that basic care here in the U.S. Large swaths of Africa do not.

And along with a low R0, the ebola virus has a relatively short infectious period — about a week. On the other hand, HIV is infectious for years and years — many of those years while the infected person has no symptoms or does not even test positive on an HIV test. The relationship between time and infection matters, too.

You Should Worry About Other Things Instead

For example, the National Institutes of Health (NIH) reports that each year, about 5,000 people under the age of 21 die in alcohol-related incidents, including car crashes, falls, burns, homicides, suicides and alcohol poisoning.

According to the Federal ReserveAmericans held $229.4 billion in consumer credit (outstanding household debt, including credit cards and loans) in July 2014.

The global sea level is rising at alarming rates, according to the National Oceanic and Atmospheric Administration (NOAA). Before 1900, these levels remained constant. Since 1900, the levels have risen 0.04 to 0.1 inches per year. But beginning in 1992, that rate climbed to 0.12 inches per year. This translates to much greater likelihood of flooding in coastal areas (including the neighborhood where I lived for 10 years).

And we should be concerned about ebola in Africa, mainly because we can do something about the higher rates of ebola infection and deaths there.

But ebola in the United States? Really, this shouldn’t be a worry for you. Let the math ease your mind.

Photo Credit: CDC Global Health via Compfight cc

Math is important in many careers, but one of the most critical is in the field of medicine.  For example, it’s very important for medicine to be dosed in correct amounts.  I’m thankful that Michelle knows her math since she is assisting physicians on a daily basis.  Even though I hope I don’t have to visit her… it’s good to know she’s there.

Can you explain what you do for a living?

I am a physician assistant. It is an advanced degree where I am able to interview, examine, order tests, perform minor procedures, assist in surgery, develop treatment plans and write prescriptions. Basically, I function much like a doctor.

When do you use basic math in your job?

All the time. I have to quickly convert pounds to kilograms because a lot of medicines are dosed in kilograms. This is especially important in trauma situations. Many medicines are weight-based like 50mg/kg divided in 3 doses per 24 hours. It gets complicated. I’m thankful that I don’t work in pediatrics because there are further calculations involving liquid and then interpreting the directions into teaspoons/mL/cc so that it makes sense to the parent based on the measuring device that is accessible to them.

Do you use any technology to help with this math?

Yes, I use calculators. I also use paper and pencil the old-fashioned way to visualize the conversions. Electronic medical record has settings that help and alert you if what you are ordering doesn’t make sense.

How do you think math helps you do your job better?

I don’t know about better, but it’s necessary.

How comfortable with math do you feel?

I rarely feel comfortable, but I feel safe that there are resources available to check my work so that I don’t make mistakes.

What kind of math did you take in high school?

I took Algebra, Geometry, and Algebra II.

Did you have to learn new skills in order to do the math you use in your job?  

No, not really. Occasionally I have to brush up on statistics in order to interpret research or scholarly articles and data. There isn’t much of a role for advanced math, such as trigonometry, in my daily job.

Questions for Michelle?  Let me know, and I’ll ask her!

With a blind, deaf, 18-year old toy poodle who has dementia (canine cognitive disorder), I’ve gotten to know our friendly neighborhood veterinarian very, very well. Dr. Robert Z. Berry, DVM at The Village Vet has helped us manage some strange symptoms and supported us in the last year since Roxie was diagnosed with dementia. Just like people doctors, vets must have excellent bedside manner, and Dr. Berry has it in spades.

I also noticed that he does quite a bit of math in his work. Roxie has been on a variety of medication, as we’ve looked for the right combination to keep her happy and healthy. And she’s only 6 pounds. That means converting measurements like crazy. At a recent visit, I finally got the idea to ask Dr. Berry to answer my Math at Work Monday questions. If your kid aspires to be a vet, read on!

Can you explain what you do for a living? 

I examine sick and healthy animals, provide preventative care such as vaccinations or parasite (intestinal and blood born worms) screening and offer early disease detection, blood tests or imaging (xrays and ultrasound). In the case of sick animals, we can hospitalize and provide medical care or medical surgical care to help return them to normal health. Additionally we provide routine surgical and dental services such as spaying , neutering, tumor removal, dental cleaning and extractions.

When do you use basic math in your job?

Everyday, from basic math skills to algebra. Here’s an example : An animal weighs 22 pounds and needs medication which is dosed at a rate of 20 mg/kg and given three times a day. The animal’s weight is measured in pounds, so the first step is to convert to kilograms. Then I need to multiply the weight in kilograms by 20 mg/kg. Now we have a milligram dose of 200 mg. But things can get even more complex. Suppose the drug is supplied in 400 mg/ml strength? I use division or an algebraic formula to arrive at a milliliter (or cc, cubic centimeter) dose of 0.5 ml.

Do you use any technology (like calculators or computers) to help with this math?  

I really prefer not to use a calculator because I think it can make my brain become lazy. It is remarkable how much agility you lose (even basic math skills) when you don’t use basic math skills on a daily basis. I calculate in my head but verify with the calculator.

How do you think math helps you do your job better?

It’s absolutely necessary with any sort of drug therapy.

How comfortable with math do you feel?

I feel very comfortable with math and have all of my life. Vets must be mentally sharp and learn to rely on their most important assets — their brains! I took calculus in high school, and I felt very confident in the class. School prepared me very adequately for the nuts-and-bolts part of my job. I was fortunate to have good teachers and also to have been raised in the time period before calculators were allowed in school. A good primary education prepares one for the rest of his or her life.

So there you have it, a vet who is both compassionate and math-savvy — a great combination! Were you surprised by the math that Dr. Berry uses in his practice? Share your response in the comments section.

When I was really young, I wanted to be a nurse. Those who know me now are probably laughing. It’s not that I’m squeamish about blood, but I absolutely cannot handle any other, um, bodily fluids. Ick. Thank goodness for people like Beth Hanes, who have made a career of caring for others who are sick or undergoing surgery. [Editors note: Since this interview appeared a year ago, Beth has decided to freelance write full time.Now that I can identify with!]

Beth Hanes is a registered nurse in a plastic surgery center.  She takes care of patients before, during and after their surgeries.  And, of course, she uses math everyday.

What kind of math do you use in your job?

I use basic math for a lot of things, but probably the most important calculations are the ones related to medication use. Sometimes I dilute medication before giving it. For example, Promethazine needs to be diluted before it’s given in an IV. Using a 10mL syringe, I draw up 1mL of Promethazine and then add 9mL of normal saline (0.9% sodium chloride) to create a 10% Promethazine solution.

I also use basic math to determine, based on body weight, how much medication to administer. Medications are generally given on a milligram per kilogram basis. So, I convert a person’s weight in pounds to weight in kilograms (divide pounds by 2.2 to obtain kilograms), then I multiply this number of kilograms by the number of milligrams per kilogram to get the correct dosage. For example, Lidocaine might be ordered as 1mg/kg. A 220-pound patient weighs 100kg, so the correct dosage is be 100mg of Lidocaine.

How do you do your calculations?

I do use calculators because they’re typically faster, but I think it’s important to know how to do math by hand. I usually don’t have a calculator on hand in the operating room! Also, it’s critically important for me to have basic formulas memorized (such as how to convert pounds to kilograms). Without that knowledge, having a calculator or not is irrelevant.

Why is math important for your job?

Math skills help me ensure patient safety. There was a highly publicized case a few years ago in which actorDennis Quaid’s infant twins were administered a very high dose of Heparin. This error occurred for many reasons, but one key factor was doing the math involved. This is a classic case of calculating dosage based on weight, and obviously errors were made in that calculation. In nursing, if you misplace a decimal point, you can kill someone.

When it comes to math in nursing, I think the main thing is to be very careful about calculations, double-check them, and then have someone else double-check them. No matter how good you may be at math, anyone can misplace a decimal point when calculating on-the-fly. It’s much better to take the extra seconds to have someone review your calculations and keep patients safe than to have any sense of ego about your math ability and endanger a patient.

What kind of math did you take in high school?

I had a rather sketchy math education, because my parents moved around a lot, and I only made it through Algebra II. On the other hand, advanced math was not yet common at the high school level when I was that age. Calculus, for example, was a college course. I did not feel I was good at math in high school. However, this “low math esteem” led me to focus on practicing real-world math skills.

These days, I am fairly comfortable with math, in general, though I frequently have to think through conversion problems, which are common in nursing. I find I often want to divide when I should multiply, for instance, so I have to be careful about that! Once I have a formula memorized, however, I feel very comfortable substituting variables with real values and arriving at the correct answer.

If you have questions for Beth, ask them in the comments section. Read other Math at Work Monday entries in the archive.  And if you or someone you know wants to be interviewed for this regular, Monday feature, let me know.

Math Appreciation Month has finally come to a close. And I thought I would end with some math that could save your life. This is serious — and I think really interesting — stuff.

If you’re seen a recent “best college degrees” list, you probably wondered two things: Why the heck is Applied Mathematics on the list, and what is it? First off, applied mathematics is not about crunching numbers. Instead, these folks use higher level mathematics — from abstract algebra to differential equations to statistics — to solve a myriad of problems in a myriad of industries. And that, my friends, is why it’s on the list. In industries like energy, cell phone technology and medicine, math modeling and statistical analysis have been applied to solve really big problems.

Math modeling is one branch of this field that has become a very big deal. Let’s say a city planner wants to know how many snow plows to buy so that the city isn’t paralyzed by a winter storm. Modeling this problem using mathematics is one way to address this problem. The way I look at it, math modeling helps us understand things we can’t see — because they’re part of situations that haven’t occurred or are too far away or are too tiny and hidden.

That too tiny and hidden part that is what math modelers are honing in on with medicine. In this field — sometimes called bioinformatics or computational biology — mathematicians help medical professionals address problems that are under the skin. Here are two examples:

Fighting Cancer: Researchers at University of Miami (UM) and University of Heidelberg in Germany have created a math model that will help oncologists predict how a tumor will grow, and even if and how it will metastasize. There have been other math models that look at tumors, but this one is different. Instead of looking at each cell or all of the cells has a big group, this model creates a kind of patchwork quilt of areas of the tumor to examine. As a result, the doctor can create a tailored plan for treating the disease that is very specific for each patient. The promise is that with specialized (rather than generalized) treatment plans will offer patients a better chance at survival.

Treating Acetaminophen OverdosesWhen a patient comes into the emergency room having overdosed on acetaminophen, the ER staff is faced with a really complex decision. Often these patients are hallucinating, unconscious or comatose. And since it’s relatively easy to overdose on the drug (it takes only five times the daily safe dosage, and acetaminophen is in many different over-the-counter and prescription medications), it’s sometimes impossible to determine when and how much of the drug was ingested. There is an antidote, but at a certain point, the doctor needs to skip that step and put the patient on the liver transplant list immediately. The trick is accurately identifying that point. University of Utah mathematician, Fred Adler, developed a set of differential equations that can better pinpoint the critical information needed to make these decisions.

In both of these cases, the math is pretty darned complicated, depending on a branch of calculus called differential equations. This approach is a step up from statistical analysis, which compares patient data to data collected from other patients. In other words, it assumes that tumors grow in the same way in all patients — which we know isn’t true. These dynamical math approaches allow doctors to offer treatments that are customized for each patient, based only on the information collected from the patient.

And the best part is that the doctors don’t have to know the math. If future studies bear out these new discoveries, a simple app can be designed for smart phones or tablets, allowing physicians to make diagnoses and treatment plans bedside.

I suspect these applications will continue to grow, as the medical community turns to mathematicians for insight into what we can’t see. That’s great news, because these advances can save lives.

I hope you’ve enjoyed what we’ve put together here for Math Appreciation Month. If you have questions, please ask them below. I’m always open to ides for future blog posts, so please share them!

Photo courtesy of fotosinteresantes

Math and cancer?  Turns out the queen of sciences can actually help doctors treat cancer in individual patients.  I looked at a particularly important study by researchers at the University of Miami and University of Heidelberg for Healthymagination, a GE-owned website that addresses health topics.

In short, researchers developed a math model to predict the growth of individual tumors in individual patients.  This is different from previous models that used statistical analysis of how tumors typically grow.  The results also predict whether or not the tumor will metastasize.

The results? Much more reliable diagnoses and treatment plans.  That’s good news for everyone.

Read my guest post here.

Do you have questions about math modeling?  Ask in the comments section.

Ronn Wade talks with a student during University of Maryland’s Mini-Med School for Kids at a summer camp in West Baltimore. (Photo courtesy of University of Maryland.)

At first glance, you might find Ronald Wade’s job a bit gruesome, but he plays a pretty important role.  As the State Anatomy Board director for Maryland, Wade is responsible for the bodies that are donated to science in Maryland.  Each year, about 1,500 cadavers are available to Maryland research facilities.  

“Anatomy is not just dissecting bodies,” he says. “Yes, a large part of what we do is to implement anatomical preparations and provide surgical areas and research equipment. But we also assist students to enhance and improve learning, and assist clinical staff to develop skills and expertise, all for the sake of the patient.” 

In our interview, he explains how he uses math in his work.

Can you explain what you do for a living?

I administer the state’s Body Donation Program, which means I carry out the disposition (cremation and burial) of Maryland’s unclaimed decedent bodies. I also provide for the transport, preparation and medical study use of those bodies to advance medical and health science through education, training and research. And I provide anatomical facilities and prepare cadavers and specimens for medical school study and for clinical use by physicians, surgeons and allied health occupations (i.e. surgical residence, trauma, paramedic & EMT training). Since I manage a public program, I provide aid and assistance to the citizens of Maryland and advance anatomical understanding and knowledge.

When do you use basic math in your job?

Because I work for the state, I manage four budgets, which requires that I calculate and forecast state appropriations revenue and expenses. Then there’s the accounting, which includes data entry for detailed ledgers and updating accounts, and managing inventories and controls. I also need to use chemical formulations to compound dilutions.

Do you use any technology to help with this math?

I do use calculators, computers.  In particular, I depend on spreadsheets and databases to perform math functions.

How do you think math helps you do your job better?
In my job, being able to perform arithmetic and math calculations with current technology is basic to minimal acceptable performance.

How comfortable with math do you feel?
It’s a matter of repetitive use and progression. Increased familiarity raises the comfort level and skill.

What kind of math did you take in high school?
I took basic math, binary systems (“new” math), algebra, calculus and accounting. I never liked math — it seemed detached to my life at the time — and was pleased just to get a passing grade.  However, I think it was because it was presented in the abstract and not so much as problem-based learning.  We should learn and teach math in such a way that takes the mystery of finding the answer but is more challenging for students!

Did you have to learn new skills in order to do the math you use in your job?
I had a basic foundation from school, which I use in my job today.

Happy Halloween everyone!  Come back on Wednesday, when we’ll start our month of nesting–with tips on home winterizing and settling in for the colder months (at least for many of us), filled with special family time.